usaco 792 lifeguards

#include <bits/stdc++.h>
#define ll long long
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pli pair<ll,int>
#define fi first
#define se second
#define inf (INT_MAX/2-1)
#define infl (1LL<<60)
#define vi vector<int>
#define pb push_back
#define sz(a) (int)(a).size()
#define all(a) begin(a),end(a)
#define y0 y5656
#define y1 y7878
#define aaa system("pause");
#define dbg(x) cerr<<(#x)<<": "<<(x)<<'\n',aaa
#define dbga(x,n) cerr<<(#x)<<"[]: ";for(int _=0;_<n;_++)cerr<<x[_]<<' ';cerr<<'\n',aaa
#define dbgs(x) cerr<<(#x)<<"[stl]: ";for(int _:x)cerr<<_<<' ';cerr<<'\n',aaa
#define dbgp(x) cerr<<(#x)<<": "<<x.fi<<' '<<x.se<<'\n',aaa
#define maxn 100000
#define maxk 100

using namespace std;

vector<pii> v, u;
int D[maxn+5][maxk+5];///d[i][j]=profit maxim daca incluzi primii i oameni, concediezi j
///din ei si il tii neaparat pe al i-lea
int d[maxn+5][maxk+5];///d[i][j]=profit max oameni 1..i concediezi j oameni
int nd[maxn+5];///=indicele ultimului interval care nu se intersecteaza cu i

void umax (int &a, int b) { a = max(a,b); }

int main () {
//  ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
  ifstream cin ("lifeguards.in");
  ofstream cout ("lifeguards.out");
  int n, k; cin >> n >> k;
  int i, j, z;
  v.resize(n);
  for (i = 0; i < n; i++) cin >> v[i].fi >> v[i].se;
  sort (all(v), [](pii a, pii b) {
        if (a.fi != b.fi) return a.fi < b.fi;
        return a.se > b.se; });
  int rm = 0, amt = 0;
  for (i = 0; i < n; i++) {
    umax(rm, v[i].se);
    if (rm == v[i].se) u.pb(v[i]);
    else amt++;
  }
  v.clear(); v.pb({0,0}); for (pii x: u) v.pb(x);
  n -= amt; k = max(k-amt, 0);
  for (i = 0, j = 1; j <= n; j++) {
    while (i+1 < j && v[i+1].se <= v[j].fi) i++;
    nd[j] = i;
  }
  for (j = 1; j <= k; j++) d[0][j] = D[0][j] = -inf;
  for (i = 1; i <= n; i++) {
    for (j = 0; j <= min(k, i-1); j++) {
      umax(D[i][j], d[nd[i]][max(0,j-(i-nd[i]-1))] + v[i].se-v[i].fi);
      ///^incluzi max pt tot ce e in fata ai sa poti adauga v[i].se-v[i].fi
      z = nd[i]+1;
      if (z < i) umax(D[i][j], D[z][max(0,j-(i-z-1))] + v[i].se-v[z].se);
      ///^incluzi primul segment care se its cu al i-lea, nu mai ai nevoie de restul
      ///pana la i
    }
    d[i][0] = D[i][0];///<--!!!
    for (j = 1; j <= min(k,i); j++) d[i][j] = max(d[i-1][j-1], D[i][j]);
  }
  cout << d[n][k];
  return 0;
}